%I #20 Jan 31 2024 14:12:16

%S 1,1,1,1,1,1,1,1,1,2,2,3,3,4,5,5,6,9,13,17,24,34,53,84,130,177,290,

%T 500,797,1300,2066,3591,6090,10298,17330,29888,50811,88358,153369,

%U 280208,481289,845090,1474535,2703811,4808816,8329214,14806743,27529781,48859783,87674040,156471632

%N Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).

%H Vaclav Kotesovec, <a href="/A359320/b359320.txt">Table of n, a(n) for n = 0..100</a>

%p f:= proc(n) local i; max(coeffs(expand(mul(1+x^(i^4), i=1..n)))) end proc:

%p map(f, [$1..50]); # _Robert Israel_, Dec 26 2022

%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(k^4)))); \\ _Michel Marcus_, Dec 26 2022

%o (Python)

%o from collections import Counter

%o def A359320(n):

%o c = {0:1,1:1}

%o for i in range(2,n+1):

%o j, d = i**4, Counter(c)

%o for k in c:

%o d[k+j] += c[k]

%o c = d

%o return max(c.values()) # _Chai Wah Wu_, Jan 31 2024

%Y Cf. A000538, A000583, A025591, A160235, A298859, A359319.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Dec 25 2022

%E a(38)-a(50) from _Seiichi Manyama_, Dec 26 2022